Question

Considere os polinômios
A (X) = x³-x ² + 1
B (x) = -2x²+3 e
C (x)=x²-x+2. Calcule.
a) A-2 . B+C
b) (A-B) ²

Answer 1

Resposta:

$A(x) =x^{3}-x^{2}+1\\B(x)=-2x^{2}+3\\C(x)=x^{2}-x+2\\ \\a)\\ \\A-2.B+C\\ \\x^{3}-x^{2}+1-2.(-2x^{2}+3)+x^{2}-x+2\\ \\x^{3}-x^{2}+1+4x^{2}-6+x^{2}-x+2\\ \\x^{3}-x^{2}+4x^{2}+x^{2}-x+1-6+2\\ \\x^{3}+4x^{2}-x-3\\ \\b)\\ \\(A-B)^{2}=[(x^{3}-x^{2}+1-(-2x^{2}+3)]^{2}\\ \\(x^{3}-x^{2}+1+2x^{2}-3)^{2}\\ \\(x^{3}+x^{2}-2)^{2}\\ \\x^{6}+x^{5}-2x^{3}+x^{5}+x^{4}-2x^{2}-2x^{3}-2x^{2}+4\\ \\x^{6}+2x^{5}+x^{4}-4x^{3}-4x^{2}+4$